Probability and Statistics

Code	8549
Year	2
Semester	S1
ECTS Credits	6
Workload	TP(60H)
Scientific area	Mathematics
Entry requirements	Calculus I and II
Mode of delivery	Face to face.
Work placements	Not applicable.
Learning outcomes	The aims of this Course Unit are: - Encourage critical skills in constructing confidence intervals, formulating hypotheses and prediction and interpreting results; - Encourage the application of probabilistic and statistical methods and techniques; -Basic - Demonstrates general culture for the Probability and Statistics: historical evolution of concepts; expertise critical sense in arguing ideas. -Scientific - Demonstrates knowledge of basic Math applied to Informatics; demonstrates basic knowledge of Probability and Statistics -Operational - Know and dominates the basic mathematical language used in Probability and Statistics; -Cross Outcomes - Understands and demonstrates general principles of ethics and morality, ability for teamwork, ability to keep records organized.
Syllabus	0. Introduction and Brief Review of Descriptive Statistics 1. Theory of probabilities 1.1 Random experiences and happenings 1.2 Conditioned probability and independence of events 1.3 Total probability theorem and T. Bayes 2. Real random variables and probability distributions 2.1 Distribution Function. properties 2.2 Discrete and continuous random variables 2.3 Parameters of a random variable 2.4 Random variables of two or more dimensions. properties 3. Theoretical models: discrete and continuous 3.1 Central Limit Theorem and its applications 3.2 De Moivre–Laplace Theorem 4 Point and interval estimation 4.1 Estimators. properties 5 Hypothesis Testing 5.1 Null hypothesis versus alternative hypothesis, p-value 6. Simple linear regression model 6.1 Least squares estimators 6.2 determination and correlation coefficient
Main Bibliography	Main bibliography: -Gonçalves, E., Nogueira, E. e Rosa, A.C. (2016). Probabilidades e Estatística para Ciências e Tecnologia. Conceitos e exercícios resolvidos. Almedina. - Montgomery, D., e Runger, G. (2011). Applied statistics and probability for engineers, 5th Edt, John Wiley & Sons. -Ross, S. (2009). Introduction to probability and statistics for engineers and scientists. Amsterdam Elsevier. - Guimarães, R. e Cabral, J. (1997). Estatística. McGraw-Hill. - Murteira, B., Ribeiro, C., Andrade e Silva, J. e Pimenta, C. (2002). Introdução à Estatística. McGraw-Hill. - Pestana, D. ,Velosa, S. (2002). Introdução à Probabilidade e à Estatística. Fundação Calouste Gulbenkian. Lisboa. -Complementary bibliography: - Mood, A., Graybill, F., and Boes, D. (1985). Introduction to the Theory of Statistics. 3rd edition. International Student Edition. - Draper, N. R., Smith, H. (1998), Applied Regression Analysis, John Wiley and Sons, 3ª Edição.
Teaching Methodologies and Assessment Criteria	The measurement of knowledge and skills acquired by students during teaching-learning is done through two frequencies (classified from 0 to 20 values) with a weighting of 0.5 each. The final teaching-learning classification (0 to 20 values) is calculated as follows: CEA=0.5F_1+0.5F_2. F_1 is the 1st test; F_2 is the 2nd test. Exemption from the final exam is granted when the final teaching-learning classification is equal to or greater than 9.5 values and attendance exceeds 40%. The “FREQUENCY” classification is awarded when the final teaching–learning grade is between 6.0 (inclusive) and 9.5 (exclusive), and it is also granted to working students and finalists. In cases where a student attains a grade exceeding 17 and wishes to retain that classification, the student is required to complete a supplementary assessment to maintain it. If the students don't attend, the grade of 17 values is guaranteed.
Language	Portuguese. Tutorial support is available in English.